⁷/₃₀
Further explanation
We will solve the problem of repeating decimals.
Definition:
A decimal number whose decimal part has digits which repeat endlessly is called a repeating decimal.
For example, \(\boxed{ \ \frac{4}{33} = 0.121212... \ }\) is a repeating decimal. The three dots mean the digits in the decimal part repeat infinitely.
Notice that when we carry out the division \(\boxed{ \ 4 \div 33 \ }\), the quotient never ends (or terminates) because zero never appears as a remainder. The block of two digits, 12, keeps appearing and no other digits appear. Often we use a bar (-) to show the block of digits which repeats in a decimal: \(\boxed{ \ \ 0. \overline{12} = 0.121212... \ \ }\)
Given:
\(\boxed{ \ 0.2333333... = 0.2\overline{3} \ }\)
Question:
Express it as a fractional form.
Problem Solving:
Let \(\boxed{ \ x = 0.2333333... \ }\)
Both sides multiplied by 10.
Then \(\boxed{ \ 10x = 2.333333... \ }\)
Let us subtract 10x by x. Subtract side by side.
\(\boxed{ \ 10x = 2.333333... \ }\)
\(\ \ \boxed{ \ \ \ \ x = 0.2333333... \ }\)
-_______________
\(\boxed{ \ \ \ 9x = 2.1 \ \ \ }\)
Therefore, \(\boxed{ \ x = \frac{2.1}{9} \rightarrow x = \frac{21}{90} \rightarrow \frac{divided \ by \ 3}{divided \ by \ 3} \rightarrow \boxed{ \ x = \frac{7}{30} \ } \ }\)
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Keywords: 0.233333 as fraction, a repeating decimals, a decimal number, repeat endlessly, infinitely, the division, the quotient, subtract, 7/30
